%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET909+1 : TPTP v9.2.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:08:57 PM UTC 2026
% Result : Theorem 0.28s 1.61s
% Output : CNFRefutation 0.38s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 42)
% Comments :
%------------------------------------------------------------------------------
fof(fc2_xboole_0,axiom,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
fof(fc3_xboole_0,axiom,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(t50_zfmisc_1,conjecture,
! [X1,X2,X3] : set_union2(unordered_pair(X1,X2),X3) != empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_zfmisc_1) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(rc2_xboole_0,axiom,
? [X1] : ~ empty(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(d2_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(d2_tarski,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(idempotence_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(rc1_xboole_0,axiom,
? [X1] : empty(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(i_0_13,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
inference(fof_simplification,[status(thm)],[fc2_xboole_0]) ).
fof(i_0_14,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
inference(fof_simplification,[status(thm)],[fc3_xboole_0]) ).
fof(i_0_15,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_16,negated_conjecture,
~ ! [X1,X2,X3] : set_union2(unordered_pair(X1,X2),X3) != empty_set,
inference(assume_negation,[status(cth)],[t50_zfmisc_1]) ).
fof(i_0_17,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
fof(i_0_18,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
fof(i_0_19,plain,
! [X51,X52,X53,X54,X55,X56,X57,X58] :
( ( ~ in(X54,X53)
| in(X54,X51)
| in(X54,X52)
| X53 != set_union2(X51,X52) )
& ( ~ in(X55,X51)
| in(X55,X53)
| X53 != set_union2(X51,X52) )
& ( ~ in(X55,X52)
| in(X55,X53)
| X53 != set_union2(X51,X52) )
& ( ~ in(esk3_3(X56,X57,X58),X56)
| ~ in(esk3_3(X56,X57,X58),X58)
| X58 = set_union2(X56,X57) )
& ( ~ in(esk3_3(X56,X57,X58),X57)
| ~ in(esk3_3(X56,X57,X58),X58)
| X58 = set_union2(X56,X57) )
& ( in(esk3_3(X56,X57,X58),X58)
| in(esk3_3(X56,X57,X58),X56)
| in(esk3_3(X56,X57,X58),X57)
| X58 = set_union2(X56,X57) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_xboole_0])])])])])]) ).
fof(i_0_20,plain,
! [X42,X43,X44,X45,X46,X47,X48,X49] :
( ( ~ in(X45,X44)
| X45 = X42
| X45 = X43
| X44 != unordered_pair(X42,X43) )
& ( X46 != X42
| in(X46,X44)
| X44 != unordered_pair(X42,X43) )
& ( X46 != X43
| in(X46,X44)
| X44 != unordered_pair(X42,X43) )
& ( esk2_3(X47,X48,X49) != X47
| ~ in(esk2_3(X47,X48,X49),X49)
| X49 = unordered_pair(X47,X48) )
& ( esk2_3(X47,X48,X49) != X48
| ~ in(esk2_3(X47,X48,X49),X49)
| X49 = unordered_pair(X47,X48) )
& ( in(esk2_3(X47,X48,X49),X49)
| esk2_3(X47,X48,X49) = X47
| esk2_3(X47,X48,X49) = X48
| X49 = unordered_pair(X47,X48) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_tarski])])])])])]) ).
fof(i_0_21,plain,
! [X60,X61] :
( empty(X60)
| ~ empty(set_union2(X60,X61)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_13])]) ).
fof(i_0_22,plain,
! [X62,X63] :
( empty(X62)
| ~ empty(set_union2(X63,X62)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_14])]) ).
fof(i_0_23,plain,
! [X32,X33] :
( ~ in(X32,X33)
| ~ in(X33,X32) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_15])]) ).
fof(i_0_24,negated_conjecture,
set_union2(unordered_pair(esk6_0,esk7_0),esk8_0) = empty_set,
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_16])])]) ).
fof(i_0_25,plain,
! [X36,X37] : set_union2(X36,X37) = set_union2(X37,X36),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(i_0_26,plain,
! [X34,X35] : unordered_pair(X34,X35) = unordered_pair(X35,X34),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(i_0_27,plain,
! [X38,X39,X40] :
( ( X38 != empty_set
| ~ in(X39,X38) )
& ( in(esk1_1(X40),X40)
| X40 = empty_set ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_17])])])])]) ).
fof(i_0_28,plain,
! [X64] : set_union2(X64,X64) = X64,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k2_xboole_0])]) ).
fof(i_0_29,plain,
~ empty(esk5_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_18])]) ).
fof(i_0_30,plain,
empty(esk4_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(i_0_31,plain,
( X3 = set_union2(X1,X2)
| ~ in(esk3_3(X1,X2,X3),X1)
| ~ in(esk3_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_32,plain,
( X3 = set_union2(X1,X2)
| ~ in(esk3_3(X1,X2,X3),X2)
| ~ in(esk3_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_33,plain,
( in(esk3_3(X1,X2,X3),X3)
| in(esk3_3(X1,X2,X3),X1)
| in(esk3_3(X1,X2,X3),X2)
| X3 = set_union2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_34,plain,
( X3 = unordered_pair(X1,X2)
| esk2_3(X1,X2,X3) != X1
| ~ in(esk2_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_35,plain,
( X3 = unordered_pair(X1,X2)
| esk2_3(X1,X2,X3) != X2
| ~ in(esk2_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_36,plain,
( in(esk2_3(X1,X2,X3),X3)
| esk2_3(X1,X2,X3) = X1
| esk2_3(X1,X2,X3) = X2
| X3 = unordered_pair(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_37,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X2 != set_union2(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_38,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_39,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_40,plain,
( empty(X1)
| ~ empty(set_union2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_21]),
[final] ).
cnf(i_0_41,plain,
( empty(X1)
| ~ empty(set_union2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_42,plain,
( X1 = X3
| X1 = X4
| ~ in(X1,X2)
| X2 != unordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_43,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_44,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_45,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_46,negated_conjecture,
set_union2(unordered_pair(esk6_0,esk7_0),esk8_0) = empty_set,
inference(split_conjunct,[status(thm)],[i_0_24]),
[final] ).
cnf(i_0_47,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_48,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_49,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_50,plain,
( in(esk1_1(X1),X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_51,plain,
set_union2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_28]),
[final] ).
cnf(i_0_52,plain,
~ empty(esk5_0),
inference(split_conjunct,[status(thm)],[i_0_29]),
[final] ).
cnf(i_0_53,plain,
empty(esk4_0),
inference(split_conjunct,[status(thm)],[i_0_30]),
[final] ).
cnf(i_0_54,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]),
[final] ).
cnf(i_0_55,axiom,
X1 = X1 ).
cnf(i_0_56,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_57,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_58,axiom,
( X1 != X2
| set_union2(X1,X3) = set_union2(X2,X3) ) ).
cnf(i_0_59,axiom,
( X1 != X2
| set_union2(X3,X1) = set_union2(X3,X2) ) ).
cnf(i_0_60,axiom,
( X1 != X2
| unordered_pair(X1,X3) = unordered_pair(X2,X3) ) ).
cnf(i_0_61,axiom,
( X1 != X2
| unordered_pair(X3,X1) = unordered_pair(X3,X2) ) ).
cnf(i_0_62,axiom,
( X1 != X2
| esk2_3(X1,X3,X4) = esk2_3(X2,X3,X4) ) ).
cnf(i_0_63,axiom,
( X1 != X2
| esk2_3(X3,X1,X4) = esk2_3(X3,X2,X4) ) ).
cnf(i_0_64,axiom,
( X1 != X2
| esk2_3(X3,X4,X1) = esk2_3(X3,X4,X2) ) ).
cnf(i_0_65,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_66,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_67,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_55_001,axiom,
X1 = X1 ).
cnf(i_0_56_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_57_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_58_004,axiom,
( X1 != X2
| set_union2(X1,X3) = set_union2(X2,X3) ) ).
cnf(i_0_59_005,axiom,
( X1 != X2
| set_union2(X3,X1) = set_union2(X3,X2) ) ).
cnf(i_0_60_006,axiom,
( X1 != X2
| unordered_pair(X1,X3) = unordered_pair(X2,X3) ) ).
cnf(i_0_61_007,axiom,
( X1 != X2
| unordered_pair(X3,X1) = unordered_pair(X3,X2) ) ).
cnf(i_0_62_008,axiom,
( X1 != X2
| esk2_3(X1,X3,X4) = esk2_3(X2,X3,X4) ) ).
cnf(i_0_63_009,axiom,
( X1 != X2
| esk2_3(X3,X1,X4) = esk2_3(X3,X2,X4) ) ).
cnf(i_0_64_010,axiom,
( X1 != X2
| esk2_3(X3,X4,X1) = esk2_3(X3,X4,X2) ) ).
cnf(i_0_65_011,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_66_012,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_67_013,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_68,plain,
( in(X1,X2)
| in(X1,X3)
| ~ in(X1,set_union2(X2,X3)) ),
inference(equality_inference,[],[37]) ).
cnf(i_0_69,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X2) ),
inference(equality_inference,[],[38]) ).
cnf(i_0_70,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(equality_inference,[],[39]) ).
cnf(i_0_71,plain,
( X1 = X2
| X1 = X3
| ~ in(X1,unordered_pair(X2,X3)) ),
inference(equality_inference,[],[42]) ).
cnf(i_0_72,plain,
~ in(X1,empty_set),
inference(equality_inference,[],[49]) ).
cnf(i_0_73,plain,
~ in(X1,set_union2(unordered_pair(esk6_0,esk7_0),esk8_0)),
inference(scs_inference,[],[i_0_46,i_0_49]) ).
cnf(i_0_74,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_49]) ).
cnf(i_0_75,plain,
empty_set = set_union2(unordered_pair(esk6_0,esk7_0),esk8_0),
inference(scs_inference,[],[i_0_46,i_0_49,i_0_56]) ).
cnf(i_0_76,plain,
in(set_union2(unordered_pair(esk6_0,esk7_0),esk8_0),set_union2(unordered_pair(empty_set,X1),unordered_pair(empty_set,X1))),
inference(scs_inference,[],[i_0_46,i_0_51,i_0_49,i_0_56,i_0_44]) ).
cnf(i_0_77,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_51]) ).
cnf(i_0_78,plain,
( X1 != unordered_pair(X2,X3)
| in(X4,X1)
| X4 != X2 ),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_79,plain,
in(set_union2(unordered_pair(esk6_0,esk7_0),esk8_0),set_union2(unordered_pair(X1,empty_set),unordered_pair(X1,empty_set))),
inference(scs_inference,[],[i_0_46,i_0_51,i_0_77,i_0_49,i_0_56,i_0_44,i_0_45]) ).
cnf(i_0_80,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_51]) ).
cnf(i_0_81,plain,
( X1 != unordered_pair(X2,X3)
| in(X4,X1)
| X4 != X3 ),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_82,plain,
esk4_0 != esk5_0,
inference(scs_inference,[],[i_0_46,i_0_51,i_0_77,i_0_52,i_0_53,i_0_49,i_0_56,i_0_44,i_0_45,i_0_67]) ).
cnf(i_0_83,plain,
~ in(X1,esk8_0),
inference(scs_inference,[],[i_0_46,i_0_51,i_0_77,i_0_47,i_0_52,i_0_53,i_0_49,i_0_56,i_0_44,i_0_45,i_0_67,i_0_38]) ).
cnf(i_0_84,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_85,plain,
( X1 != set_union2(X2,X3)
| in(X4,X1)
| ~ in(X4,X2) ),
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_86,plain,
~ in(X1,unordered_pair(esk6_0,esk7_0)),
inference(scs_inference,[],[i_0_46,i_0_51,i_0_77,i_0_47,i_0_84,i_0_52,i_0_53,i_0_49,i_0_56,i_0_44,i_0_45,i_0_67,i_0_38,i_0_39]) ).
cnf(i_0_87,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_88,plain,
( X1 != set_union2(X2,X3)
| in(X4,X1)
| ~ in(X4,X3) ),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_89,plain,
in(set_union2(unordered_pair(esk6_0,esk7_0),esk8_0),unordered_pair(empty_set,X1)),
inference(scs_inference,[],[i_0_46,i_0_51,i_0_77,i_0_47,i_0_84,i_0_52,i_0_53,i_0_49,i_0_56,i_0_44,i_0_45,i_0_67,i_0_38,i_0_39,i_0_68]) ).
cnf(i_0_90,plain,
( ~ in(X1,set_union2(X2,X3))
| in(X1,X2)
| in(X1,X3) ),
inference(rename_variables,[],[i_0_68]) ).
cnf(i_0_91,plain,
~ in(X1,set_union2(set_union2(empty_set,empty_set),set_union2(empty_set,empty_set))),
inference(scs_inference,[],[i_0_46,i_0_72,i_0_51,i_0_77,i_0_80,i_0_47,i_0_84,i_0_52,i_0_53,i_0_49,i_0_56,i_0_44,i_0_45,i_0_67,i_0_38,i_0_39,i_0_68,i_0_37]) ).
cnf(i_0_92,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_51]) ).
cnf(i_0_93,plain,
( X1 != set_union2(X2,X3)
| in(X4,X2)
| in(X4,X3)
| ~ in(X4,X1) ),
inference(rename_variables,[],[i_0_37]) ).
cnf(i_0_94,plain,
~ in(esk4_0,set_union2(unordered_pair(esk5_0,esk5_0),unordered_pair(esk5_0,esk5_0))),
inference(scs_inference,[],[i_0_46,i_0_72,i_0_51,i_0_77,i_0_80,i_0_92,i_0_47,i_0_84,i_0_52,i_0_53,i_0_49,i_0_56,i_0_44,i_0_45,i_0_67,i_0_38,i_0_39,i_0_68,i_0_37,i_0_42]) ).
cnf(i_0_95,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_51]) ).
cnf(i_0_96,plain,
( X1 != unordered_pair(X2,X3)
| X4 = X2
| X4 = X3
| ~ in(X4,X1) ),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_97,plain,
in(set_union2(unordered_pair(esk6_0,esk7_0),esk8_0),set_union2(unordered_pair(empty_set,X1),X2)),
inference(scs_inference,[],[i_0_46,i_0_72,i_0_51,i_0_77,i_0_80,i_0_92,i_0_47,i_0_84,i_0_52,i_0_53,i_0_49,i_0_56,i_0_44,i_0_45,i_0_67,i_0_38,i_0_39,i_0_68,i_0_37,i_0_42,i_0_69]) ).
cnf(i_0_98,plain,
( ~ in(X1,X2)
| in(X1,set_union2(X2,X3)) ),
inference(rename_variables,[],[i_0_69]) ).
cnf(i_0_99,plain,
in(set_union2(unordered_pair(esk6_0,esk7_0),esk8_0),set_union2(X1,unordered_pair(empty_set,X2))),
inference(scs_inference,[],[i_0_46,i_0_72,i_0_51,i_0_77,i_0_80,i_0_92,i_0_47,i_0_84,i_0_52,i_0_53,i_0_49,i_0_56,i_0_44,i_0_45,i_0_67,i_0_38,i_0_39,i_0_68,i_0_37,i_0_42,i_0_69,i_0_70]) ).
cnf(i_0_100,plain,
( ~ in(X1,X2)
| in(X1,set_union2(X3,X2)) ),
inference(rename_variables,[],[i_0_70]) ).
cnf(i_0_101,plain,
esk4_0 != set_union2(esk5_0,esk5_0),
inference(scs_inference,[],[i_0_46,i_0_72,i_0_51,i_0_77,i_0_80,i_0_92,i_0_95,i_0_47,i_0_84,i_0_52,i_0_53,i_0_49,i_0_56,i_0_44,i_0_45,i_0_67,i_0_38,i_0_39,i_0_68,i_0_37,i_0_42,i_0_69,i_0_70,i_0_57]) ).
cnf(i_0_102,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_51]) ).
cnf(i_0_103,plain,
~ in(set_union2(esk4_0,esk4_0),set_union2(unordered_pair(esk5_0,esk5_0),unordered_pair(esk5_0,esk5_0))),
inference(scs_inference,[],[i_0_46,i_0_72,i_0_51,i_0_77,i_0_80,i_0_92,i_0_95,i_0_102,i_0_47,i_0_84,i_0_52,i_0_53,i_0_49,i_0_56,i_0_44,i_0_45,i_0_67,i_0_38,i_0_39,i_0_68,i_0_37,i_0_42,i_0_69,i_0_70,i_0_57,i_0_65]) ).
cnf(i_0_104,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_51]) ).
cnf(i_0_105,plain,
~ in(X1,set_union2(esk8_0,esk8_0)),
inference(scs_inference,[],[i_0_46,i_0_72,i_0_51,i_0_77,i_0_80,i_0_92,i_0_95,i_0_102,i_0_104,i_0_47,i_0_84,i_0_52,i_0_53,i_0_49,i_0_56,i_0_44,i_0_45,i_0_67,i_0_38,i_0_39,i_0_68,i_0_37,i_0_42,i_0_69,i_0_70,i_0_57,i_0_65,i_0_66]) ).
cnf(i_0_106,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_51]) ).
cnf(i_0_107,plain,
( in(esk3_3(esk5_0,esk5_0,esk4_0),esk4_0)
| in(esk3_3(esk5_0,esk5_0,esk4_0),esk5_0) ),
inference(scs_inference,[],[i_0_46,i_0_72,i_0_51,i_0_77,i_0_80,i_0_92,i_0_95,i_0_102,i_0_104,i_0_47,i_0_84,i_0_52,i_0_53,i_0_49,i_0_56,i_0_44,i_0_45,i_0_67,i_0_38,i_0_39,i_0_68,i_0_37,i_0_42,i_0_69,i_0_70,i_0_57,i_0_65,i_0_66,i_0_33]) ).
cnf(i_0_108,plain,
( X1 = set_union2(X2,X3)
| in(esk3_3(X2,X3,X1),X1)
| in(esk3_3(X2,X3,X1),X2)
| in(esk3_3(X2,X3,X1),X3) ),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_109,plain,
( ~ in(esk4_0,esk3_3(esk5_0,esk5_0,esk4_0))
| in(esk3_3(esk5_0,esk5_0,esk4_0),esk5_0) ),
inference(scs_inference,[],[i_0_46,i_0_72,i_0_51,i_0_77,i_0_80,i_0_92,i_0_95,i_0_102,i_0_104,i_0_47,i_0_84,i_0_52,i_0_53,i_0_49,i_0_56,i_0_44,i_0_45,i_0_67,i_0_38,i_0_39,i_0_68,i_0_37,i_0_42,i_0_69,i_0_70,i_0_57,i_0_65,i_0_66,i_0_33,i_0_43]) ).
cnf(i_0_110,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_112,plain,
~ in(X1,set_union2(empty_set,empty_set)),
inference(scs_inference,[],[i_0_51,i_0_49]) ).
cnf(i_0_113,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_51]) ).
cnf(i_0_114,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_49]) ).
cnf(i_0_115,plain,
X1 = set_union2(X1,X1),
inference(scs_inference,[],[i_0_51,i_0_113,i_0_49,i_0_56]) ).
cnf(i_0_116,plain,
$false,
inference(scs_inference,[],[i_0_86,i_0_48,i_0_51,i_0_113,i_0_49,i_0_56,i_0_44]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET909+1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.33 % Computer : n028.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 02:39:46 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 0.28/1.61 % Version : CSE_E---1.7
% 0.28/1.61 % Problem : theBenchmark.p
% 0.28/1.61 % SZS status Theorem for theBenchmark.p
% 0.28/1.61 % SZS output start CNFRefutation
% See solution above
% 0.38/1.77 % Total time : 1.272s
%------------------------------------------------------------------------------